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  • Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 10

Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.5 question 10

Answers (1)

Answer:  10^{\log \sin x} \times \log 10 \times \cot x

Hint: Diff by 10^{x}

Given: 10^{\log \sin x}

Solution:  Let y=10^{\log \sin x}        .........(1)

Taking log both sides

        \begin{aligned} &\log y=\log 10^{\log \sin x} \\\\ &\log y=\log \sin x \log 10 \end{aligned}
Differentiate w.r.t x,

        \begin{aligned} &\frac{1}{y} \frac{d y}{d x}=\log 10 \frac{d}{d x} \log \sin x \\\\ &\frac{1}{y} \frac{d y}{d x}=\log 10 \frac{1}{\sin x} \frac{d}{d x} \sin x \end{aligned}

        \begin{aligned} &\frac{1}{y} \frac{d y}{d x}=\log 10\left(\frac{1}{\sin x}\right) \cos x \\\\ &\frac{d y}{d x}=y(\log 10 \cdot \cot x) \\\\ &\frac{d y}{d x}=10^{\log \sin x} \times \log 10 \times \cot x \end{aligned}        ......[Using (1)]

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